Finite Group DatabasebetaFinite Group Databasebeta| order | 666 |
| isoclinism | isoclinic class of D3×C37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D3×C37⋊C3 |
| unambiguous semidirect product | C3⋊(C2×C37⋊C3) |
| unambiguous semidirect product | (D3×C37)⋊C3 |
| Fitting, socle, derived | C3×C37 ⋊ C2×C3 |
| Hall | C3×C37⋊C3 ⋊ C2 |
| Sylow | C37 ⋊ C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C37 | C2×C3 |
| LCS | G ▷ C3×C37 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 111 |
45 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D37⋊C3, C2×D3×C37⋊C3, D9×C37⋊C3, … |
| maximal normal subgroup of | D3×D37⋊C3, C2×D3×C37⋊C3, D3×#66526, … |
| maximal quotient of | Dic3×C37⋊C3, C2×D3×C37⋊C3, D9×C37⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(666, 10);